Dice Stepping

Dice Stepping is when you improve a random number generator by widening the range.

Speak bloody Common, will ye?

It means boosting roll with d6s up to using d8s, or d8s to d10s, whatever is the next larger die on the table. You can also penalize a roll by stepping down -- d8 down to d6, or d6 down to d4.

Examples:

• Weapons in Advanced Dungeons & Dragons (1st edition) would step down their damage dice when used against large-sized targets such as giants or dragons. A notable exception was the two-handed sword, which went from 1d10 against man-sized targets to 3d6 against large targets. There were plenty of polearms that also stepped up against large targets, but who the hell used a fauchard-fork or bill-guisarme outside of jokes?
  • Actually, longswords did d10 instead of d8, and even short swords did d8 instead of d6. SWORDS FOR EVERYBODY!!11!!one!!
    • Actually, no they didn't. Longswords did d12 to large opponents in Advanced Dungeons & Dragons (1st edition)
• Weapons in Dungeons & Dragons 3rd Ed would step down damage if they were "small" versions built for halflights or gnomes, and up for "large" weapons for ogres and goliaths.
• Tristat DX (aka BESM) uses d6 for stats by default, but you could step down to d4 if you wanted to play a TristatDX version of Bunnies and Burrows, or you could step up to d20s for playing in a superhero genre.
• Cortex System uses it, so you'll see it in the Firefly and Battlestar Galactica RPGs.
• The Usagi Yojimbo game uses it. It's the godless overlap of weeaboo, furfags, fa/tg/uys and this wiki page.
• Savage Worlds system uses dice stepping for ranks of character traits. Typical people have d6 strength, but your mastery of the Charles Atlas method could get you a d10 or d12 for your strength trait.
• Ironclaw Dice stepping is integral to resolution mechanics, however unlike other systems where the dice are added together, the highest die rolled is kept as the result. So you may have a D8 and a D4 against your opponents two D6, if you flub your d8 roll on a 1 that D4's 4 might just save you.

Does it work?

Mathfag says: Some, but it's not huge; you get about the same odds as if you kept the same die but added the difference in their mean values (these odds are identical if the die step is 2: d6 to d8, or d10 to d12). I.E.: 1d6+1 and 1d8 give identical chances of rolling more than 1d6 -- you'll never roll 8 on d6+1, but you'll never roll a 1 either. What dice stepping is really good for is giving your players more feeling of an improvement than just +1 ("d00d, like, 8 is bigger than 1"). It also gives the players the opportunity to fondle bigger dice, since they love rolling dice, and bigger dice feel more like testicles.

Odds of rolling higher than the next smaller die in the chart
d3	d4	d6	d8	d10	d12	d20
-	50%	58.33%	56.25%	55%	54.17%	67.5%

Odds of rolling higher on a 1dY when compared to a smaller 1dX+M is
(2Y-X-1)/(2Y) (X <= Y) for M=0
(2Y-2M-X-1)/(2Y) (X+M <= Y)

Die	Mean Value	Chance of this or better
		1	2	3	4	5	6	7	8	9	10	11	12
d3	2	100%	66%	33%
d4	2.5	100%	75% +9%	50% +17%	25% +25%
d6	3.5	100%	83% +8%	66% +16%	50% +25%	33% +33%	17% +17%
d8	4.5	100%	88% +5%	75% +9%	63% +13%	50% +17%	38% +21%	25% +25%	13% +13%
d10	5.5	100%	90% +2%	80% +5%	70% +7%	60% +10%	50% +12%	40% +15%	30% +17%	20% +20%	10% +10%
d12	6.5	100%	92% +2%	83% +3%	75% +5%	67% +7%	58% +8%	50% +10%	42% +12%	33% +13%	25% +15%	17%	8%
d20	10.5	100%	95% +3%	90% +7%	85% +10%	80% +13%	75% +17%	70% +20%	65% +23%	60% +27%	55% +30%	50% +33%	45% +37%